The term The Theory of Rings seems first used as title of a book by Jacobson [43], and in his
preface Jacobson asserts that the theory that forms the subject of the book had its beginning …

We discuss a new attack, termed a dimension or linear decomposition attack, on several
known group-based cryptosystems. This attack gives a polynomial time deterministic …

This paper introduces a new type of attack, termed a nonlinear decomposition attack,
against two known group-based key agreement protocols, namely, protocol based on …

Let k be a (commutative) field, and k< X1,•••, Xn> the free associative algebra in n (non-
commuting) variables. Denote by Mi the ideal of k< X1,.••, Xn> generated by all monomials …

In this paper, we introduce two general schemes of algebraic cryptography. We show that
many of the systems and protocols considered in literature that use two-sided multiplications …

In this survey, we describe a general key exchange protocol based on semidirect product of
(semi) groups (more specifically, on extensions of (semi) groups by automorphisms), and …

The linear decomposition attack provides a serious obstacle to direct applications of
noncommutative groups and monoids (or semigroups) in cryptography. To overcome this …

This book is concerned qith algebraic cryptography, where the design and analysis of
cryptographic schemes are based on algebraic structures: nonabelian groups, rings …

Let R be a finite unital commutative ring. We introduce a new class of finite groups, which we
call hereditary groups over R. Our main result states that if G is a hereditary group over R …

Содержит теоретические основы и описания известных теоретико-числовых и
алгебраических конструкций в криптологии. Приводятся схемы, системы и протоколы …